Quantum channel decomposition with pre- and post-selection

• URL: http://arxiv.org/abs/2305.11642v2
• Date: Tue, 29 Aug 2023 00:51:14 GMT
• Title: Quantum channel decomposition with pre- and post-selection
• Authors: Ryo Nagai, Shu Kanno, Yuki Sato, Naoki Yamamoto
• Abstract summary: This paper proposes a channel decomposition method for target unitaries that have their input and output conditioned on specific quantum states. We explicitly determine the requisite number of decomposing channels, which could be significantly smaller than the selection-free scenario. We demonstrate an application of this approach to the quantum linear solver algorithm, highlighting the efficacy of the proposed method.
• Score: 0.7597059965024503
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum channel decomposition techniques, which contain the so-called probabilistic error cancellation and gate/wire cutting, are powerful approach for simulating a hard-to-implement (or an ideal) unitary operation by concurrently executing relatively easy-to-implement (or noisy) quantum channels. However, such virtual simulation necessitates an exponentially large number of decompositions, thereby significantly limiting their practical applicability. This paper proposes a channel decomposition method for target unitaries that have their input and output conditioned on specific quantum states, namely unitaries with pre- and post-selection. Specifically, we explicitly determine the requisite number of decomposing channels, which could be significantly smaller than the selection-free scenario. Furthermore, we elucidate the structure of the resulting decomposed unitary. We demonstrate an application of this approach to the quantum linear solver algorithm, highlighting the efficacy of the proposed method.

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